VakhitovKolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields

abstract

• We study the linear stability of localized modes in self-interacting spinor fields, analyzing the spectrum of the operator corresponding to linearization at solitary waves. Following the generalization of the Vakhitov--Kolokolov approach, we show that the bifurcation of real eigenvalues from the origin is completely characterized by the Vakhitov--Kolokolov condition $dQ/domega=0$ and by the vanishing of the energy functional. We give the numerical data on the linear stability in the generalized Gross--Neveu model and the generalized massive Thirring model in the charge-subcritical, critical, and supercritical cases, showing the agreement with the Vakhitov--Kolokolov and the energy vanishing conditions.

authors

• Berkolaiko, Gregory

published proceedings

• Nonlinearity

author list (cited authors)

• Berkolaiko, G., Comech, A., & Sukhtayev, A.

citation count

• 13

complete list of authors

• Berkolaiko, Gregory||Comech, Andrew||Sukhtayev, Alim

publication date

• March 2015

publisher

• IOP Publishing  Publisher

published in

• NONLINEARITY  Journal

keywords

• 49 Mathematical Sciences
• 4902 Mathematical Physics

Digital Object Identifier (DOI)

• 10.1088/0951-7715/28/3/577

start page

• 577

end page

• 592

volume

• 28

issue

• 3